The present invention relates to an ink jet print head for discharging ink drops from ink outlets by use of thermal energy.
Recently, in contrast with the wire dot printing methods, non-impact recording method is attracting interest because the recording noise level is negligible. In particular, an ink jet recording method is attractive as it permits high-speed recording on ordinary paper without the need of a deposition treatment on the paper side. In the field, therefore, aiming at an optimal ink discharge performance, various approaches have been made, with associated implementations.
In the ink jet recording method, a recording is effected with discharged droplets of recording liquid, called xe2x80x9cink;xe2x80x9d deposited on a recordable material. This method is categorized into several systems according to the manner in which the drops of recording liquid are formed.
FIG. 1 illustrates a bubble jet recording system as a conventional example. The conventional system includes a substrate 32 provided with a heating resistor 30, a channel plate member 36 for defining an ink supply path 34, and an orifice plate 40 formed with an orifice as an ink outlet 38 communicating with the ink supply path 34. The heating resistor 30 rapidly heats to vaporize a volume of ink supplied on a heating zone surrounding the resistor 30, causing ink bubbles 42 to grow, exerting pressures therearound so that an ink drop is discharged from the ink outlet 38, with trailing droplets 50, 52 as shown in FIG. 2.
Grown bubbles 42 become deflated as they are cooled by surrounding ink, and fade out with ink vapour therein condensed to be liquidated.
A consumed volume of ink by the discharge is supplemented from an ink pool through the ink supply path 34, due to capillary forces acting on an ink meniscus 44 retreating inside the ink outlet 38.
To permit a high-speed recording, it is desirable to repeat a discharge of an ink drop in a short period, supplementing at a high speed a volume of ink consumed during every discharge through the ink outlet 38.
In a conventional implementation, the diameter of the ink outlet 38 is reduced to have an increased capillary force, and the channel resistance of the ink supply path 34 is reduced.
Thus, ink is supplemented at an increased speed, and with an increased momentum, which causes, as shown in FIG. 1, an elongated ink pillar 46 to project from the ink outlet 38, before it deforms into an ink drop. In the deformation, the elongated ink pillar 46 is broken so that a leading upper portion is changed into a main drop 48 and a trailing lower portion is separated into a number of relatively large low-speed satellites 50, 52 such as in FIG. 2. Such satellites adversely affect the printing.
Moreover, as a volume of ink is supplemented with an increased momentum, as shown in FIG. 3, an ink meniscus 44 at a top end of the ink outlet 38 has an increased tendency to convex outside and concave inside of the outlet 38. The meniscus 44 thus vibrates with a reduced damping ratio. That is, the vibration of the meniscus 44 is not readily stopped.
As the ink discharge is repeated in a short period, a subsequent discharge occurs immediately after the supplement of ink, so that it may occur when the ink meniscus 44 starts convexing above the ink outlet. This causes an undesirable deformation of an ink drop and an undesirable development of low-speed satellites, resulting in a reduced quality of recording.
Further, some volume of ink may flood over a surface area around the ink outlet 38, causing an ink drop to be discharged in an oblique direction, or bubbles to be involved, stopping the discharge, with a reduced reliability of recording.
A probable solution to such problems may include entering subsequent discharge after a sufficient damping of vibration, which however is inconsistent with an intended high-speed recording.
The present invention has been achieved with such points in mind.
It therefore is an object of the present invention to provide an ink jet print head with criteria such as on an sectional area of an ink outlet and a fluid resistance of an ink supply path to achieve an optimal high-speed ink discharge with an increased reliability and an improved cost effect. without additional elements.
In the present invention, an ink outlet is tapered, with a gradually reduced diameter, toward an orifice plate surface. Supposing a straight aperture of a diameter, it is typical that the quantity Q of an ink drop discharged from a print head of an identical resolution is substantially identical, as well as the volume of a void defined by an ink outlet and an ink meniscus drawn back therein just after a discharge of an ink drop, i.e., the quantity Qr of ink to be supplemented.
Letting tr be a time for the drawn back ink meniscus to restore to an exit level of the ink outlet, and v be a mean flow velocity in the ink outlet,
v=Qr/(Axc2x7tr). 
Letting xcfx81 be an ink density, and M be a mean momentum per unit volume,
M=xcfx81xc2x7Qr/(Axc2x7tr) 
Thus, the larger the diameter of the ink outlet is, the smaller the mean momentum becomes, with a reduced frequency of occurrence of an overshooting ink meniscus.
As the overshooting meniscus convexes like a paraboloid of revolution, letting Qo be an overshooting volume of ink and h be an overshooting height or projection of ink,
h=2xc2x7Qo/A. 
Thus, the larger the diameter of the ink outlet is, the smaller the overshooting volume of ink becomes.
For a quantity of ink supplemented in a time, the larger the diameter of the ink outlet is, the overshooting ink might have the smaller projection h. However, experiments showed that the projection h of an ink overshoot depends on a sectional configuration of the ink supply path, i.e., a channel resistance or flow resistance thereof.
This fact means that an optimized relationship between an ink outlet sectional area and a channel resistance permits a high-speed recording without low-speed satellites.
The inventors found that a subsequent discharge of ink immediately after a concaved meniscus of the ink has restored to an exit level of an ink outlet can be free from an undesirable deformation of a drop of the ink, when an overshooting height or projection h of the ink falls within a range such that:
0 less than h less than 0.3(q/A), 
where q is a quantity in volume of the ink drop, and A is a sectional area at the exit level of the ink outlet.
The present invention is based on this fact.
Thus, to achieve the object, a genus of the present invention provides an ink jet print head comprising a substrate member formed with a heating resistor, an ink path defining member provided on the substrate member, for defining an ink supply path including a heating zone in a vicinity of the heating resistor, and an orifice plate member formed with an ink outlet communicating with the ink supply path and laminated on the substrate member, with the ink path defining member interposed therebetween, the ink jet print head generating heat from the heating resistor to discharge a drop of ink from the ink outlet, the ink supply path having a fluid resistance so that a relationship is established such that 0 less than h less than 0.3(q/A), where q is a quantity of the drop of the ink, A is a sectional area at an exit level of the ink outlet, and h is a maximal projection that a meniscus of the ink has when it projects from the ink outlet after it has restored the exit level from a retreat position it had after the drop of the ink had been discharged.
According to a species of the genus of the invention, the relationship is established such that:
xcfx80{(3q)/(4xcfx80)}⅔xe2x89xa6Axe2x89xa6xcfx80{(3q)/(2xcfx80)}⅔. 
This is because of the following reason.
An undesirable overshooting height becomes smaller as the ink outlet has an increased diameter. The ink outlet diameter may preferably be increased.
If the ink outlet has a small diameter, a volume of ink extruded to be discharged therefrom constitutes an elongated ink pillar, which has a reduced tendency to be deformed to constitute an ink drop due to surface tensile forces of the ink so that it is ruptured into droplets, thus causing satellite drops to degrade a print quality.
To avoid such a rupture, letting d be a diameter of an ink outlet and D be a diameter of an expected ink drop, it is preferable that:
dxe2x89xa7Dxe2x80x83xe2x80x83(a). 
Letting q be a volume of the ink drop,
q=(4xcfx80/3)(D/2)3xe2x80x83xe2x80x83(b). 
Thus, letting A be a transverse sectional area of the ink outlet, it so follows that:
A=xcfx80(D/2)2xe2x80x83xe2x80x83(c). 
From the expressions (a), (b) and (c),
Axe2x89xa7xcfx80{(3q)/(4xcfx80))}⅔xe2x80x83xe2x80x83(d). 
On the other hand, if the ink outlet diameter is excessively large, a discharged ink drop has a reduced velocity with a reduced momentum susceptible to disturbances, causing an ink flying direction to be deviated or an air bubble to be involved.
To ensure a normal ink flying direction, it is preferable for the ink outlet to function as a nozzle for extruding a volume of ink in a direction normal to an orifice plate so that a lateral side of the extruded ink is perpendicular to a top surface of the orifice plate, which means the extruded ink has a volume q equivalent to or larger than a volume of a hemisphere having the same diameter d as the ink outlet.
It thus so follows that:
qxe2x89xa7(4xcfx80/3)(d/2)3xc3x97xc2xdxe2x80x83xe2x80x83(e). 
From the expressions (c) and (e),
Axe2x89xa6xcfx80{(3q)/(2xcfx80))}⅔xe2x80x83xe2x80x83(f). 
Thus, from the expressions (d) and (f),
xcfx80{(3q)/(4xcfx80))}⅔xe2x89xa6Axe2x89xa6xcfx80{(3q)/(2xcfx80))}⅔xe2x80x83xe2x80x83(g). 
The ink outlet may have an arbitrary sectional form other than a cicle, e.g. it may have a polygonal section. The expression (g) is applicable also to such an arbitrary form, as it has a mean sectional area when assumed as a circle equivalent in area.
According to another species of the genus of the invention, another relationship is established such that 0.9xc3x97t1 less than tmin less than 1.1xc3x97t1, where t1 is a time for the meniscus of the ink to restore to the exit level from the retreat position, and tmin is a minimal period by which the ink jet print head discharges the drop of the ink.
According to the present invention, after an ink drop is discharged from an ink outlet by grown bubbles, the projection of a meniscus at ink refill is kept small by optimizing the channel resistance value of an ink supply path. Therefore, the periodic damping time of the meniscus becomes short, and the unfavorable effect to be caused at the subsequent discharge is avoided.
Moreover, in the case in which the sectional area of the ink outlet is set large within the predetermined range, the projection of the meniscus at ink refill becomes small, and the damping time of the vibration of the meniscus becomes short.
Further, in a constitution in which the relation between the restoring time of the meniscus and the minimum driving period of a print head is set within the predetermined range, no dead time exists before the subsequent discharge without an undesirable deformation of the discharged ink drop, and the discharge interval becomes short.